Analysis of parity-violating electron scattering on deformed nuclei

Parity-violating electron scattering (PVES) offers an important and model-independent method for probing the nuclear neutron density distributions. In this paper, a deformed PVES model is constructed, and detailed analyses of parity-violating asymmetry APV are presented for ²⁰⁸Pb and ²⁷Al. The impacts of the deformation of neutron and proton distributions (βₙ and βₚ) on APV are revealed by the plane- and distorted-wave Born approximations, respectively. It is demonstrated that βₙ mainly affects the depth of the diffraction minima of APV, while βₚ influences the width of the diffraction minima of APV. Furthermore, we combine the deformed mean-field model and deformed PVES calculations to modify the linear relation between the neutron skin thickness ΔRₙₚ and APV that accommodates the correlation between the weak charge radius RW and APV. Based on the latest PVES experimental measurements, ΔRₙₚ and RW are extracted from the improved linear correlations. The studies in this paper provide new insights into determining βₙ and can serve as a useful guide for future PVES experiments.